$p$-adic field search results

Results (7 matches)

 

Label	$n$	Polynomial	$p$	$e$	$f$	$c$	Galois group	$u$	$t$	Visible slopes	Slope content	Unram. Ext.	Eisen. Poly.	Ind. of Insep.	Assoc. Inertia
5.6.0.1	$6$	$x^{6} + x^{4} + 4 x^{3} + x^{2} + 2$	$5$	$1$	$6$	$0$	$C_6$ (as 6T1)	$6$	$1$	$[\ ]$	$[\ ]^{6}$	$t^{6} + t^{4} + 4 t^{3} + t^{2} + 2$	$x - 5$	$[0]$	$[]$
5.6.3.1	$6$	$x^{6} + 60 x^{5} + 1221 x^{4} + 8846 x^{3} + 9864 x^{2} + 29208 x + 29309$	$5$	$2$	$3$	$3$	$C_6$ (as 6T1)	$3$	$2$	$[\ ]$	$[\ ]_{2}^{3}$	$t^{3} + 3 t + 3$	$x^{2} + 20 x + 5$	$[0]$	$[1]$
5.6.3.2	$6$	$x^{6} + 75 x^{2} - 375$	$5$	$2$	$3$	$3$	$C_6$ (as 6T1)	$3$	$2$	$[\ ]$	$[\ ]_{2}^{3}$	$t^{3} + 3 t + 3$	$x^{2} + 5 t$	$[0]$	$[1]$
5.6.4.1	$6$	$x^{6} + 12 x^{5} + 54 x^{4} + 122 x^{3} + 168 x^{2} + 228 x + 233$	$5$	$3$	$2$	$4$	$S_3$ (as 6T2)	$2$	$3$	$[\ ]$	$[\ ]_{3}^{2}$	$t^{2} + 4 t + 2$	$x^{3} + 5$	$[0]$	$[1]$
5.6.4.2	$6$	$x^{6} + 10 x^{3} - 25$	$5$	$3$	$2$	$4$	$S_3\times C_3$ (as 6T5)	$6$	$3$	$[\ ]$	$[\ ]_{3}^{6}$	$t^{2} + 4 t + 2$	$x^{3} + 5 t + 15$	$[0]$	$[1]$
5.6.5.1	$6$	$x^{6} + 5$	$5$	$6$	$1$	$5$	$D_{6}$ (as 6T3)	$2$	$6$	$[\ ]$	$[\ ]_{6}^{2}$	$t + 3$	$x^{6} + 5$	$[0]$	$[2]$
5.6.5.2	$6$	$x^{6} + 10$	$5$	$6$	$1$	$5$	$D_{6}$ (as 6T3)	$2$	$6$	$[\ ]$	$[\ ]_{6}^{2}$	$t + 3$	$x^{6} + 10$	$[0]$	$[2]$